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Graphing Quadratic Functions: Understanding Parabolas

Learn about the standard form of quadratic functions and how to graph parabolas, find vertices, determine maximum and minimum points, and identify characteristics. Explore examples and practice problems.

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Graphing Quadratic Functions: Understanding Parabolas

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  1. 9-1 Notes for Algebra 1 Graphing Quadratic Functions

  2. 9-1 pg. 550 22-56e, 81-92(x3)

  3. Quadratic Functions (Standard Form, where ) The shape is Non-linear called a parabola Parabolas are symmetric about a central line called the axis of symmetry. The axis of symmetry intersects the parabola at only one point called the vertex.

  4. Maximum and Minimum When , the parabola opens up the vertex is called the minimum (because it is the lowest point). When , the parabola opens down the vertex is called the maximum (because it is the highest point).

  5. Graphing the parabolas To find the x-coordinate of the vertex use The is . Make a table with 2 units smaller and 2 units larger than the of the vertex, then solve for the .

  6. Example 1: Graph a parabola 1.) Use a table of values to graph . State the domain and range.

  7. Example 1: Graph a parabola 1.) Use a table of values to graph . State the domain and range. D

  8. Example 2: Identify Characteristics from Graphs Find the vertex, the equation of the axis of symmetry, and y-intercept. 1.) 2.)

  9. Example 2: Identify Characteristics from Graphs Find the vertex, the equation of the axis of symmetry, and y-intercept. 1.) 2.)

  10. Example 3: Identify Characteristics from Equations Find the vertex, the equation of the axis of symmetry and y-intercept. 1.) 2.)

  11. Example 3: Identify Characteristics from Equations Find the vertex, the equation of the axis of symmetry and y-intercept. 1.) 2.)

  12. Example 4: Maximum and Minimum Values Consider . a.) Determine whether the function has a maximum or a minimum value. b.) State the maximum or minimum value of the function. c.) State the domain and range of the function.

  13. Example 4: Maximum and Minimum Values Consider . a.) Determine whether the function has a maximum or a minimum value. b.) State the maximum or minimum value of the function. c.) State the domain and range of the function.

  14. Example 5: Graph Quadratic Functions Graph

  15. Example 5: Graph Quadratic Functions Graph

  16. Example 6: Use a Graph of a Quadratic Function ARCHERY Ben shoots an arrow. The height of the arrow can be modeled by , where represents the height in feet of the arrow seconds after it is shot into the air. 1.) Graph the height of the arrow. 2.) At what height was the arrow shot? 3.) What is the maximum height of the arrow?

  17. Example 6: Use a Graph of a Quadratic Function ARCHERY Ben shoots an arrow. The height of the arrow can be modeled by , where represents the height in feet of the arrow seconds after it is shot into the air. 1.) Graph the height of the arrow. 2.) At what height was the arrow shot? 3.) What is the maximum height of the arrow?

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